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Exploring S3 and P3 Manifolds: A Visual Guide

Dive into the fascinating world of S3 and P3 manifolds. Understand their construction and visualize their properties through simple yet powerful analogies. Discover the unique topology of these spaces.

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Exploring S3 and P3 Manifolds: A Visual Guide

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  1. Manifolds and Cobordism Mark Behrens

  2. Manifolds

  3. Manifolds

  4. Manifolds

  5. Manifolds

  6. Manifolds

  7. Manifolds

  8. Manifolds

  9. S3 is obtained by taking a solid ball and gluing the opposite hemispheres together: Glue

  10. You can think of S3 this way: If you are flying around in S3, and fly through the surface in the northern hemisphere, you reemerge in the southern hemisphere.

  11. P3 is obtained by taking a solid ball and gluing antipodal points together: Glue

  12. You can think of P3 this way: If you are flying around in P3, and fly through the surface in the northern hemisphere, you reemerge in the southern hemisphere, but flipped backwards.

  13. You can think of P3 this way: If you are flying around in P3, and fly through the surface in the northern hemisphere, you reemerge in the southern hemisphere, but flipped backwards.

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